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Characteristic solutions of polynomial-like iterative equations

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In this paper we study characteristic theory of polynomial-like iterative equations in the general case where multiple characteristic roots may be involved. We describe such an equation in linear difference form, give relations between the characteristic solutions and other solutions, and give a construction of all continuous solutions in some cases. We also show that the equation has no continuous real solutions, if it has no real characteristic roots.

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Manuscript received: March 25, 2002 and, in final form, June 2, 2003.

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Yang, D., Zhang, W. Characteristic solutions of polynomial-like iterative equations . Aequ. Math. 67, 80–105 (2004).

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Mathematics Subject Classification (2000).